if a + 2*b = 5, show that :- cube of a + 8*cube of b + 30*a*b = 125
provide detailed proof

Well, your first equation is:

a + 2b = 5

Since you see the cubed functions... well, cube all of them:

(a + 2b)^3 = 5^3

Then, expand ans simplify. You should get your answer.

You'll see you'll have terms in a^2b and ab^2 too, use your initial equation to substitute a and b for one of those terms.

Tell us what you got! :)